Allan MacLeod's web pages

[Hugo Pfoertner]

SeqFans,
(cc to Allan MacLeod) 

starting from two discussions on diophantine equations in the newsgroup
sci.math.research
http://groups.google.com/group/sci.math.research/msg/1a119c5fe095e240
http://groups.google.com/group/sci.math.research/msg/995d7f89ab33fb5d
I arrived at Allan MacLeod's web pages "ELLIPTIC CURVES in RECREATIONAL
NUMBER THEORY" 
http://maths.paisley.ac.uk/allanm/ECRNT/Ecrnt.htm , news: 
http://maths.paisley.ac.uk/allanm/ecrnt/news.htm
and found many candidates for new sequences, like the following example:

LEECH'S PROBLEM:
http://maths.paisley.ac.uk/allanm/ecrnt/leech/leechint.htm
http://maths.paisley.ac.uk/allanm/ecrnt/leech/LEECH.pdf

What is a preferred way to transform tables like
http://maths.paisley.ac.uk/allanm/ecrnt/leech/leechres
into OEIS entries? The table starts:

SOLUTIONS TO LEECH'S PROBLEM FOR 2 <= N <= 999

 b^2 + h^2 = c^2   b^2 + (N h)^2 = d^2

 N    b   h

 7   12   5 
10   24   7 
11   21  20 
12   45  28 
14   15   8 
17  528 455 
19 1155  68 
22   40   9 
23  468 595 
27   60  11 
28  455 528
..  ... ...
 
Would 3 sequences be appropriate, e.g.

A1xxxxx
Values of N for which Leech's problem "Find two rational right-angled
triangles on the same base whose heights are in the ratio N:1" has a
solution.
7,10,11,12,14,17,19,22,23,27,28,

Bases of right triangles that are solutions to Leech's problem A1xxxxx
12,24,21,45,15,528,1155,40,458,60,455,

Heights of right triangles that are solutions to Leech's problem A1xxxxx
5,7,20,28,8,455,68,9,595,11,528,

or would it be better to create a fancy table:

Parameter triples [N,b,h] for which Leech's problem "Find two rational
right-angled triangles on the same base b whose heights h are in the
ratio N:1" has a solution.
7,12,5, 10,24,7, 11,21,20, 12,45,28, 14,15,8, 
17,528,455, 19,1155,68, 22,40,9, 23,468,595, 
27,60,11, 28,455,528

The same question is applicable to many similar cases from Allan
MacLeod's web pages, which definitely deserve some massive harvesting
effort. Certainly there are many here in the seqfan community having a
better background knowledge on diophantine equations than I have.

It seems that currently only the "Knight's problem" is covered in the
OEIS:
http://www.research.att.com/~njas/sequences/A085514 (plus 3 sequences
for x,y,z)
http://www.research.att.com/~njas/sequences/A086446

http://www.research.att.com/~njas/sequences/A102535
http://www.research.att.com/~njas/sequences/A102778
http://www.research.att.com/~njas/sequences/A102779
http://www.research.att.com/~njas/sequences/A102809

The technique used in A085514 and A102535 is similar to the first
suggestion made above, e.g. to use separate sequences for the
parameters.

Hugo Pfoertner